These aren't Bechet's earliest recordings of the 20s, which are also really rad, but dude basically kept the same agenda throughout his career. Blues is extremely prevalent here, as many of these compositions are based on the 12-bar form and feature extensive pentatonic improvisation.
What's important, though, is Bechet's ability to think ahead in his solos. It's one thing to be able to string chords together throughout your improvisation. It's another to have clear statements that all have something to do with each other and make sense together any which way you want to connect them. It's like looking at, I don't know, a fucking Nautilus or something, which, on its own, is a creature that looks just completely wild as fuck. And then you sort of think about coral reefs as a whole and what other insane beasts dwell there, and the whole thing really just makes your brain seem so goddamn pathetic. But then you realize what a magnificent flesh computer you have bouncing around in your skull, and everything falls into place. What I'm saying is that Sidney Bechet's playing is like evolution.
Bechet mostly follows chords around with his huge vibrato, and throws in tons of diminished runs which I'm just a big giant sucker for. Maple Leaf Rag ~2:20 for a nice break Yngwie Malmsteen would be jealous of.
Also check out this version of Summertime. Fucking heavy. Put it on: yr moshing.